1. Field of the Invention
The present invention relates to spline interpolation for a projection image display apparatus, and more particularly, to a convergence adjusting apparatus and method for adjusting convergence using selective spline interpolation.
2. Description of the Related Art
With increasing demands for larger image display apparatuses, as well as higher image quality apparatuses, projection-type image display apparatuses have been proposed for attaining large-screen display. In particular, a technique for adjusting convergence is an important factor that mostly influences image quality and productivity of a projection television.
A projection television has three independent cathode ray tubes (CRTs), i.e., red (R), green (G), and blue (B), unlike a general direct-view television. Therefore, in order to form an image from the R/G/B CRTs, it is necessary to control convergence for making focuses of the R/G/B beams to coincide with one another. One method of adjusting the convergence is to use forty seed points that are arranged on a seed matrix of eight horizontal seeds and five vertical seeds. The sections between the seed points are associated with curves set by sequential spline interpolation. However, according to the conventional scheme of the sequential spline interpolation, curves symmetrical left and right cannot be obtained under the condition in which operations are performed with respect to seed points closest to a convergence controlled seed point.
Referring to FIGS. 1 and 2 showing a conventional spline interpolation scheme employing a sequential operation method, a three-dimensional equation, f(x)=Y+KX+AX2+BX3 is obtained using two seed points, and a relatively gentle curve is set between the two seed points. In obtaining the three-dimensional equation, parameters X and Y are predetermined positional coordinate values, and K is a differential value at the coordinate seed X, i.e., a slope of the curve. Thus, it is possible to obtain the respective coefficients and to plot curves between each of seed points shown in FIG. 1.
According to the conventional spline interpolation scheme employing a sequential operation method, as shown in FIG. 1, if a value of Seed 3 moves up to a seed point P1, a sequential operation is conducted using spline interpolation. First, in a section {circle around (1)}, a slope at Seed 1 is calculated using the coordinate values of Seed 1 and Seed 2, and coefficients K1, Y1, A1, and B1 are obtained from the three-dimensional equation. Also, in a section {circle around (2)}, a slope at Seed 2 is established using the coordinate values of Seed 2 and Seed 3, and coefficients K2, Y2, A2, and B2, which are coefficients at Seed 2, are set, accordingly. In such a manner, sequential operations are carried out in the sections {circle around (1)} through {circle around (4)}.
On the other hand, in the case of performing a sequential operation as shown in FIG. 2, during a spline interpolation for Seed 2 in the section {circle around (2)}, Seed 1 and Seed 3 are employed in establishing the three-dimensional equation passing through Seed 2. After the spline operation, the slope at Seed 2, K2, and three coefficients, Y2, A2, and B2, are different from the previous values. Thereafter, a spline operation for Seed 3 in a section {circle around (3)} is associated with the coefficients of Seed 2 that are the changed values of K2, Y2, A2, and B2 and coefficients of Seed 4, K4, Y4, A4, and B4.
However, such a sequential operation may cause errors in convergence adjustment because it results in an asymmetrical curve to the left and right due to different seed values between the left and right sides of an operated seed.